The text inside a text box can (and usually should) have a style applied to it.

Linking more than two text boxes

Multiple text boxes can be linked to make a chain of three or more. Do that by selecting the last box in the current chain and linking it to the next empty box.

Sadly, there’s no way to link multiple boxes at once.

Text is a single linked block

The text in linked text boxes is treated as a single entity by Word. Click inside a linked text box and press Ctrl + A (Select All) will select all the text in all linked text boxes (and not select text outside the boxes).

Text inside boxes all selected with a single Ctrl + A shortcut.

That makes it easy to reformat all the text.

But linked text boxes are not linked in other ways

Create Link only applies to text. Nothing else about the text boxes are linked.

A change in the look or size of a text box has no effect on any linked box.

Nor are text boxes grouped in the selection pane

Break the link

To unlink text boxes, click in the first or source text box then Format | Text | Break Link.